Normal-to-characteristic subgroup property

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

Definition

Symbol-free definition

A subgroup property is said to be normal-to-characteristic if its logical conjunction with the subgroup property of being normal is the subgroup property of being characteristic.

In other, words, a subgroup property is said to be normal-to-characteristic if every normal subgroup satisfying the property must be characteristic.